TY - GEN
T1 - Approximate general responses of tuned and mistuned 4-degree-of-freedom systems with parametric stiffness
AU - Sapmaz, Ayse
AU - Acar, Gizem D.
AU - Feeny, Brian F.
N1 - Publisher Copyright:
© The Society for Experimental Mechanics, Inc. 2019.
PY - 2019
Y1 - 2019
N2 - The purpose of this study is to find approximate solutions to tuned and mistuned 4-DOF systems with parametric stiffness. In this work, the solution and stability of four-degree-of-freedom Mathieu-type system will be investigated. To find the broken-symmetry system response, Floquet theory with harmonic balance will be used. A Floquet-type solution is composed of a periodic and an exponential part. The harmonic balance is applied to the original differential equation of motion. The analysis brings about an eigenvalue problem. By solving this, the Floquet characteristic exponents and the corresponding eigenvectors that give the Fourier coefficients are found in terms of the system parameters. The stability transition curve can be found by analyzing the real parts of the characteristic exponents. The frequency content can be determined by analyzing imaginary parts at the exponents. A response that involves single Floquet exponent (and its complex conjugate) can be generated with a specific set of initial conditions, and can be regarded as a modal response. The method is applied to both tuned and detuned four-degree-of-freedom examples.
AB - The purpose of this study is to find approximate solutions to tuned and mistuned 4-DOF systems with parametric stiffness. In this work, the solution and stability of four-degree-of-freedom Mathieu-type system will be investigated. To find the broken-symmetry system response, Floquet theory with harmonic balance will be used. A Floquet-type solution is composed of a periodic and an exponential part. The harmonic balance is applied to the original differential equation of motion. The analysis brings about an eigenvalue problem. By solving this, the Floquet characteristic exponents and the corresponding eigenvectors that give the Fourier coefficients are found in terms of the system parameters. The stability transition curve can be found by analyzing the real parts of the characteristic exponents. The frequency content can be determined by analyzing imaginary parts at the exponents. A response that involves single Floquet exponent (and its complex conjugate) can be generated with a specific set of initial conditions, and can be regarded as a modal response. The method is applied to both tuned and detuned four-degree-of-freedom examples.
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U2 - 10.1007/978-3-319-74700-2_35
DO - 10.1007/978-3-319-74700-2_35
M3 - Conference contribution
AN - SCOPUS:85061375260
SN - 9783319746999
T3 - Conference Proceedings of the Society for Experimental Mechanics Series
SP - 315
EP - 324
BT - Topics in Modal Analysis and Testing, Volume 9 - Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics 2018
A2 - Mains, Michael
A2 - Dilworth, Brandon J.
T2 - 36th IMAC, A Conference and Exposition on Structural Dynamics, 2018
Y2 - 12 February 2018 through 15 February 2018
ER -